Reflection: Developing a Conceptual Understanding Investigating Special Quadrilaterals - Section 3: Investigation: Properties of Special Quadrilaterals


Since the Common Core asks us to completely rethink transformations in the Geometry curriculum, one of my goals this year has been to infuse transformations as a thematic yearlong thread.  For this reason, I modified the Data Record Sheet students would use in the investigation.  Instead of asking students to use rulers to measure the lengths of sides and diagonals or to use protractors to measure the angles (which is time consuming and sometimes frustrating), I encouraged students to instead use tracing paper.  

Before launching the task, I told students that the big idea for the activity was to see how line and rotational symmetry could help them to make sense of the sides, angles, and diagonals of special quadrilaterals.  

When debriefing this task, I made sure to use tracing paper to show how one side of a kite, for example, mirrors the other.  Since the diagonal connecting the kite's vertex angles acts as a line of symmetry, this helps us understand how one half of the kite maps onto the other half, which is why one pair of angles is congruent and why there are two pairs of congruent sides.  Similarly, I used tracing paper to show how a parallelogram's rotational symmetry helps us to understand why opposite sides and opposite angles are congruent.  The intersection of a parallelogram's diagonals is the center of rotation, and a rotation of 180 degrees maps the opposite sides and angles onto each other. 

  Developing a Conceptual Understanding: Using a Transformations Lens to Make Sense of Properties of Special Quadrilaterals
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Investigating Special Quadrilaterals

Unit 2: Introducing Geometry
Lesson 4 of 8

Objective: Students will be able to investigate features of special quadrilaterals (angles, sides, diagonals, symmetries) and list the properties of these special quadrilaterals.

Big Idea: In this hands-on investigation, students will explore properties of special quadrilaterals and ultimately come up with a minimal defining list to differentiate them from one another.

  Print Lesson
Math, Geometry, deductive reasoning, definition, basic properties
  95 minutes
inv sp quad rotated li
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